We test the proposed methodology in the Stanford bunny [1]}, obtained from the software MeshMixer. This mesh has 5,550 vertices and 10,996 triangles, which results in 15,404,025 pairs of distance to be learned. We randomly select 50,000 pairs (0.32% of the total pairs) as training data, for which we compute the exact geodesic distance [2]}. We use the 50 eigenfunctions associated with the lowest eigenvalues of the Laplace-Beltrami operator to define \(\mbox{$v$}{}(\mbox{$x$}{}_i)\) . Both for the trunk and branch network, we use 10 hidden layers of 200 neurons each. We train for 50,000 iterations with ADAM [3]} with exponential decay of the learning rate. To demonstrate the potential of this method, we also compute geodesic paths between \(\mbox{$x$}{}_1\)  and \(\mbox{$x$}{}_2\)  by solving the following initial value problem:
\(\dot{\mbox{$x$}{}} &=& - \nabla _{\mbox{$x$}{}} d(\mbox{$x$}{},\mbox{$x$}{}_2)\\\mbox{$x$}{}(0) &=& \mbox{$x$}{}_1\) 
